Problem: Baby Ehab was toying around with arrays. He has an array a of length n. He defines an array to be good if there's no way to partition it into 2 subsequences such that the sum of the elements in the first is equal to the sum of the elements in the second. Now he wants to remove the minimum number of elements in a so that it becomes a good array. Can you help him?

A sequence b is a subsequence of an array a if b can be obtained from a by deleting some (possibly zero or all) elements. A partitioning of an array is a way to divide it into 2 subsequences such that every element belongs to exactly one subsequence, so you must use all the elements, and you can't share any elements.

Input

The first line contains an integer n (2 ≤ n ≤ 100) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_{n} (1 ≤ a_i ≤ 2000) — the elements of the array a.

Output

The first line should contain the minimum number of elements you need to remove.

The second line should contain the indices of the elements you're removing, separated by spaces.

We can show that an answer always exists. If there are multiple solutions, you can print any.

Examples

Input


4
6 3 9 12


Output


1
2

Input


2
1 2


Output


0

Note

In the first example, you can partition the array into [6,9] and [3,12], so you must remove at least 1 element. Removing 3 is sufficient.

In the second example, the array is already good, so you don't need to remove any elements.

Solution (in JAVA):

Solution:
//package graphs;
import java.util.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class PW {
	
	public static int arr[];
	public static int memo[][];
	public static FastReader s = new FastReader();
	public static void main(String[] args) {
		// TODO Auto-generated method stub
	
		
		int t=1;
		//int k=0;
		while(t-- >0)
		{
			
			
			int n=s.nextInt();
		     
		     int  arr[]=new int[n];
		     int sum = 0;
		     long even=0, odd = 0;
		     long p2 = 0,p4 = 0;
		     for(int i=0;i<n;i++){
		          arr[i]=s.nextInt();
		     }
		     int gcd = (int)arr[0];
		     int  pre[]=new int[n];
		     for(int i=1;i<n;i++){
		          gcd = (int)(gcd(gcd,arr[i]));
		     }
		     for(int i=0;i<n;i++){
		          pre[i] = arr[i]/gcd;
		     }
		     for(int i=0;i<n;i++){
		          sum += pre[i];
		          if(pre[i]%2==1){
		               odd++;
		          }
		     }
		     if(sum%2 == 1){
		          System.out.println("0");
		          return;
		     }
		     memo=new int[101][200005];
		     for(int i=0;i<memo.length;i++)
		    	 Arrays.fill(memo[i], -1);
		     boolean ans = helper(pre,0,sum/2);
		     if(ans==false){
		          System.out.println(0);
		          return;
		     }
		     System.out.println(1);
		     for(int i=0;i<n;i++){
		          if(pre[i]%2 == 1){
		               System.out.println(i+1);
		               return;
		          }
		     }
			
		}
		
	
	}
	
	public static boolean helper(int arr[], int i, int sum){
	     if(sum == 0){
	          return true;
	     }
	     if(i>=arr.length || sum < 0){
	          return false;
	     }
	     if(memo[i][sum] != -1){
	          return memo[i][sum]==0?false:true;
	     }
	     boolean ans1 = helper(arr,i+1,sum-arr[i]);
	     boolean ans2 = helper(arr,i+1,sum);
	     boolean fin=ans1||ans2;
	     if(fin==true)
	    	 memo[i][sum]=1;
	     else
	    	 memo[i][sum]=0;
	     return fin ;
	}
	
//	public static long fastExpo(long a, long n, long mod) {
//		  long result = 1;
//		  while (n > 0) {
//		    if ((n & 1)>0)
//		      result = (result * a) % mod;
//		    a = (a * a) % mod;
//		    n >>= 1;
//		  }
//		  return result;
//		}
//	1  4   8
	
	public static int digit(int n)
	{
		int c=0;
		while(n!=0)
		{
			n/=10;
			c++;
		}
		return c;
	}
	 
	public static int rev(String n)
	{
		String ans="";
		for(int i=n.length()-1;i>=0;i--)
			ans=ans+n.charAt(i);
		
		return Integer.valueOf(ans);
	}
	 
	public static boolean solve(HashMap<Integer,Integer> mp1,HashMap<Integer,Integer> mp2)
	{
		for(int i:mp2.keySet())
		{
			if(!mp1.containsKey(i))
				return false;
			
			if(mp1.get(i)<mp2.get(i))
				return false;
		}
		
		return true;
		
	}
	
	
	public static int count(int b[]){
		  int s = 0;
		  for (int i = 0; i < 32; i++) {
		    if(b[i]>0){
		      s |= (1<<i);
		    }
		  }
		  return s;
		}
	
	public static void remove(int b[], int val){
		  for (int i = 0; i < 32; i++) {
		    if(((val>>i)&1)==1)
		      b[i]--;
		  }
		}
	
	public static void add(int b[], int val){
		  for (int i = 0; i < 32; i++) {
		    if(((val>>i)&1)==1)
		      b[i]++;
		  }
		}
	    public static String largestNumber( List<String> ab) {
	        
	       // List<String> ab= new ArrayList<>();
	       // for(int i=0;i<A.size();i++)
	       // {
	       //     ab.add(String.valueOf(A.get(i)));
	       // }
	        
	        Collections.sort(ab, new Comparator<String>(){ 
	            
	            public int compare(String X, String Y) { 
	          
	        // first append Y at the end of X 
	        String XY=X + Y; 
	          
	        // then append X at the end of Y 
	        String YX=Y + X; 
	          
	        // Now see which of the two formed numbers  
	        // is greater 
	        return XY.compareTo(YX)>0?-1:1; 
	            
	                
	            }
	            
	            
	            
	        });
	        StringBuilder abc= new StringBuilder();
	        
	        
	        for(int i=0;i<ab.size();i++)
	        {
	           abc.append(ab.get(i));
	            
	        }
	        if(abc.length()==0)
	            return abc.toString();
	        
	        if(abc.charAt(0)=='0')
	        return "0";
	        else
	        return abc.toString();
	        
	    }
	
	public static boolean pal(String s)
	{
		int i=0;
		int j=s.length()-1;
		while(i<=j)
		{
			if(s.charAt(i)!=s.charAt(j))
				return false;
			i++;
			j--;
		}
		return true;
	}
	
	
	
	
	static class FastReader {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            br = new BufferedReader(
                new InputStreamReader(System.in));
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt() { return Integer.parseInt(next()); }
 
        long nextLong() { return Long.parseLong(next()); }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

	
	public static long solve(int n, int r)
    {


        long p = 1, k = 1;
        if (n - r < r) {
            r = n - r;
        }
 
        if (r != 0) {
            while (r > 0) {
                p *= n;
                k *= r;
 
                long m = __gcd(p, k);
 
                
                p /= m;
                k /= m;
 
                n--;
                r--;
            }
 
           
        }
        else {
            p = 1;
        }
 
        
        //System.out.println(p);
        return p;
    }
	
	
	public static long gcd(long a,long b)
	{
		if(a==0||b==0)
			return a+b;
		return gcd(b,(a%b));
	}
	
	public static long __gcd(long n1, long n2)
    {
        long gcd = 1;
 
        for (int i = 1; i <= n1 && i <= n2; ++i) {
            // Checks if i is factor of both integers
            if (n1 % i == 0 && n2 % i == 0) {
                gcd = i;
            }
        }
        return gcd;
    }
	
	public static boolean prime(int n)
	{
		if(n<=2)
			return true;
		
		for(int i=2;i<=Math.sqrt(n);i++)
		{
			if(n%i==0)
				return false;
		}
		
		return true;
		
	}
	public static long fastExpo(long a,long n,long mod){
        if (n == 0)
            return 1;
        else{
            long x = fastExpo(a,n/2,mod);
            if ((n&1) == 1){
                return (((a*x)%mod)*x)%mod;
            }
            else{
                return (((x%mod)*(x%mod))%mod)%mod;
            }
        }
    }
}
class pair{
	//public:
		int f;
		int s;
		pair(int x,int y)
		{
			f=x;
			s=y;
		}
        
}